Conventionally, a wireless communication channel in a single-carrier transmission system is modeled as having a time-varying impulse response g(τ,t), which may be frequency selective for any given time t due to multipaths. The channel's frequency selectivity can be estimated by observing the known pilot signal transmitted during the time of interest whereas the time selectivity is usually tracked by observing multiples of these periodically inserted known signals.
However, in a land mobile communication environment, the channel's selectivity is mainly caused by movement of the terminal. For as long as the velocity of the movement remains constant, the channel can be modeled by a time-invariant delay-Doppler response h(τ,ν), which represents the complex-valued channel gain of the scatterer incurring a delay τ and Doppler shift ν to the incoming signal. For various reasons, this fact has been used mostly as a design limitation on the frequency of pilot insertion in the time domain to avoid aliasing. Slightly more sophisticated usage of the Doppler information may be found in the channel tracking related filter design that requires the estimation of the channel's Doppler spread.
A time-frequency hopping pattern is a signal whose frequency contents change as a function of time, either periodically or non-periodically, in a specific manner. Time-frequency hopping signals have been used in many communication and radar applications. Recently, due to popular adaptation of Orthogonal Frequency Division Multiplexing (OFDM) as the multiple technology in future wireless communication systems, the potential for using them as synchronization signals has been under extensive investigation. Since an OFDM system essentially divides the radio resource into orthogonal time-frequency units, it is natural to design synchronization signals that conform with existing time-frequency partition.
In an OFDM system, pilot symbols are placed periodically in the time-frequency plane for channel estimation. FIG. 1 shows an example of a regularly spaced pilot pattern, denoted φ=0, and a Costas array pattern, denoted φ=1, which is one of many possible variations resulting from shifting the horizontal scan lines of the regularly spaced pilot pattern in a particular order, as is well known for a skilled person in the art. Costas array patterns are disclosed in “Medium Constraints on Sonar Design and Performance”, by J. P. Costas, in EASCON Cony. Rec., 1975, pp 68A-68L.
Each cell in the array represents one of the Nfft sub-carriers in an OFDM symbol, which has an interval of Ts sec. including Tcp sec. of cyclic prefix. Thus, the sub-carrier spacing is fs=1/(Ts−Tcp) Hz. For the original regularly spaced pattern, one pilot symbol is inserted every N OFDM symbols in the time domain, i.e. Tp=NTs and every M sub-carriers in the frequency domain, i.e. fp=Mfs. Each pattern may have a sub-carrier offset index 0≦φ≦M with respect to the first sub-carrier.
Any pilot pattern may be specified by a two-dimensional time-frequency array whose element C[n, m] is the complex value of the pilot symbol transmitted on the m'th sub-carrier in the n'th OFDM symbol. Unless otherwise stated, C[n,m] is “1” if a pilot symbol is present and “0” if not. The corresponding continuous-time signal of the pilot pattern over Q time domain periods can be expressed as a sequence of OFDM symbols by:
                                          s            p                    ⁡                      (            t            )                          =                              ∑                          n              =              0                                      QN              -              1                                ⁢                                          ⁢                                    c              n                        ⁡                          (                              t                -                                  nT                  s                                            )                                                          (        1        )                        where                                                                            c            n                    ⁡                      (            t            )                          =                              ∑                          i              =              0                                                      N                fft                            -              1                                ⁢                                          ⁢                                                    c                n                            ⁡                              [                i                ]                                      ⁢                          μ              ⁡                              (                                  t                  -                                      iT                    c                                                  )                                                                        (        2        )            is the n'th OFDM symbol that further consists of a sequence cn[i] modulating the transmit filter pulsing function μ(t). Ignoring cyclic prefix, the pilot pattern's time-frequency array representation C[n,m] is related to the discrete-time sequence cn[i] by
                                          C            ⁡                          [                              n                ,                m                            ]                                =                                    ∑                              i                =                0                                                              N                  fft                                -                1                                      ⁢                                                  ⁢                                                            c                  n                                ⁡                                  [                  i                  ]                                            ⁢                              ⅇ                                                      j2π                    ⁢                    mi                                                        N                    fft                                                                                      ,                  m          =          0                ,        1        ,        …        ⁢                                  ,                              N            fft                    -          1                                    (        3        )            
To demodulate the data symbols in an OFDM system, the receiver needs to know the channel's time-frequency response H(t,f), which is the two-dimensional Fourier transform of the delay-Doppler response h(τ,ν). If sufficient numbers of the base pilot signals are observed over time and frequency, the output of the delay-Doppler correlator is a good approximation of the delay-Doppler response.
The channel is modeled as having a delay-Doppler response h(τ,ν), which represents the complex-valued channel gain of the scatterer incurring a delay τ and Doppler shift ν to the incoming signal. Assuming that the radio environment consists of a continuum of scatterers (or “targets”), each introduces a certain delay and Doppler shift to the signal propagating through it, the received signal corresponding to the pilot is given then by:r(t)=∫ν0ν0+νmax∫τ0τ0+τmaxh(τ,ν)sp(t−τ)ej2πνtdτdν+z(t)  (4)where z(t) is the Additive White Gaussian Noise (AWGN), τ0 and ν0 are the initial timing and frequency offset respectively, and
                                                        τ              max                        ≤                          1                              f                p                                              =                                    1                              Mf                s                                      =                                                            T                  s                                -                                  T                  cp                                            M                                      ⁢                                  ⁢                                            v              max                        ≤                          1                              T                p                                              =                      1                          NT              s                                                          (        5        )            are the maximum delay and Doppler spread of the channel that are smaller than or equal to the values that can be supported by the pilot's density without aliasing.
Present detectors normally use correlator matched to hypothesized signals and then find peaks and compare them with a certain threshold to determine the presence of the pilot signals. This correlation process may be too computationally complex especially when there are a large number of potential hypotheses.
A known system that uses time-frequency hopping patterns as synchronization signals is disclosed in U.S. Pat. No. 6,961,364 B1, by Laroia et al. Different base stations use patterns with different slopes, and the detection algorithm is a maximum energy detector.